## PRP Records

### Probable Primes Top 10000

#### (293510 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 6001 2^352228-18953 106032 Enzo Doria 05/2013 6002 (2^352223+1118)/2 106030 Stefano Morozzi 09/2020 6003 (2^352212+2250)/2 106027 Stefano Morozzi 01/2021 6004 (2^352136+2638)/2 106004 Stefano Morozzi 09/2020 6005 2^352107+1872533 105995 Enzo Doria 05/2016 6006 (2^352096+2086)/2 105992 Stefano Morozzi 09/2020 6007 2^352066-2591 105983 Yves Minet 07/2014 6008 2^352030+715 105972 Lelio R Paula 10/2011 6009 9*6^136176-5 105967 Lelio R Paula 11/2014 6010 17099*2^351991+58329 105965 Paul Vanderveen 12/2017 6011 28582^5097+5097^28582 105963 Hans Havermann 09/2020 6012 155^48377+2 105962 Lelio R Paula 08/2013 6013 (23*10^105944-119)/3 105945 Robert Price 07/2021 6014 2^351865+1869707 105922 Enzo Doria 05/2016 6015 24974^17427+17427^24974 105921 Hans Havermann 09/2020 6016 25163^16194+16194^25163 105920 Hans Havermann 09/2020 6017 2^351831+23 105912 Lelio R Paula 10/2011 6018 (2^351818+3798)/2 105908 Stefano Morozzi 02/2021 6019 9*2^351784-5 105899 Lelio R Paula 09/2014 6020 (2^351776+2766)/2 105895 Stefano Morozzi 01/2021 6021 (85*10^105881+203)/9 105882 Robert Price 09/2020 6022 2^351671-112387 105864 Enzo Doria 06/2014 6023 2^351669-109501 105863 Enzo Doria 04/2014 6024 2^351644+74731 105856 Enzo Doria 04/2016 6025 13^95025-42 105853 Lelio R Paula 12/2016 6026 2^351599+15015 105842 Lelio R Paula 01/2017 6027 19^82763+90 105834 Lelio R Paula 01/2017 6028 (205*10^105831-1)/3 105833 Robert Price 11/2021 6029 26050^11551+11551^26050 105832 Hans Havermann 09/2020 6030 (9179*2^351540-1)/221 105826 Lelio R Paula 05/2015 6031 20^81329-51 105812 Lelio R Paula 01/2017 6032 (5*10^105811+211)/9 105811 Robert Price 02/2018 6033 2^351483+28425 105807 Lelio R Paula 01/2017 6034 25231^15610+15610^25231 105804 Hans Havermann 09/2020 6035 15^89960+86 105802 Lelio R Paula 02/2017 6036 2^351460-17289 105801 Enzo Doria 05/2013 6037 19^82735+22 105798 Lelio R Paula 01/2017 6038 2^351435-109077 105793 Enzo Doria 04/2014 6039 2^351393+1089 105780 Lelio R Paula 01/2017 6040 2^351364+72631 105772 Enzo Doria 04/2016 6041 (2^351333+3626)/2 105762 Stefano Morozzi 09/2020 6042 26818^8783+8783^26818 105761 Hans Havermann 09/2020 6045 2^351305+1872467 105754 Enzo Doria 05/2016 6044 3^221649+16 105754 Lelio R Paula 11/2016 6043 32511^1790+1790^32511 105754 Hans Havermann 09/2020 6046 8*3^221637-5 105749 Lelio R Paula 09/2014 6047 2^351279-2780449 105746 Enzo Doria 03/2016 6048 (2^351263+3198)/2 105741 Stefano Morozzi 09/2020 6049 15^89903-26 105735 Lelio R Paula 02/2017 6051 2^351213-73 105726 Lelio R Paula 10/2011 6050 (2^351214+1210)/2 105726 Stefano Morozzi 09/2020 6052 2^351192-4589 105720 Yves Minet 07/2011 6053 20^81250-33 105709 Lelio R Paula 12/2016 6054 (2^351133+3530)/2 105702 Stefano Morozzi 09/2020 6055 (2^351103+534)/2 105693 Stefano Morozzi 09/2020 6056 2^351076-113159 105685 Enzo Doria 07/2014 6057 93^53688-2 105684 Lelio R Paula 09/2013 6058 2^351060-4559 105680 Yves Minet 07/2011 6059 ((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9 105676 Hans Havermann 08/2019 6060 11^101473-750 105674 Enzo Doria 11/2012 6061 3*5^151181-8 105672 Lelio R Paula 11/2014 6062 15^89831-34 105650 Lelio R Paula 02/2017 6064 11^101448-360 105648 Enzo Doria 08/2012 6063 3*7^125011+4 105648 Lelio R Paula 11/2014 6065 2^350943-113269 105645 Enzo Doria 07/2014 6066 2*10^105636-91 105637 Robert Price 04/2020 6067 24231^22880+22880^24231 105634 Hans Havermann 09/2020 6068 35296^983+983^35296 105626 Hans Havermann 09/2020 6069 2^350868-19725 105622 Enzo Doria 06/2013 6070 2^350858-59291 105619 Enzo Doria 10/2015 6071 2^350851+135 105617 Lelio R Paula 10/2011 6072 2^350841-741 105614 Lelio R Paula 01/2017 6073 3*10^105582+77 105583 Robert Price 09/2018 6074 24915^17284+17284^24915 105581 Hans Havermann 09/2020 6075 (5*10^105576-53)/3 105577 Robert Price 09/2020 6076 8*10^105571+3 105572 Robert Price 08/2015 6077 2^350674-78557 105564 Jorge Menendez 03/2018 6078 2*5^151026-3 105563 Lelio R Paula 11/2014 6079 (2^350702+5)/34264674063 105562 Lelio R Paula 12/2013 6080 6^135647-5^135647 105554 Jean-Louis Charton 02/2009 6081 3^221211+236 105545 Lelio R Paula 11/2016 6082 (32*10^105530-77)/9 105531 Robert Price 06/2018 6083 10^105515+33 105516 Lelio R Paula 11/2016 6084 24644^19125+19125^24644 105516 Hans Havermann 10/2020 6085 10^105515-41033 105515 Patrick De Geest 12/2016 6086 (29*2^350473-1)/267927 105499 Lelio R Paula 03/2014 6087 2^350455-430567 105498 Harrison Mesh 06/2022 6088 17^85732-72 105489 Lelio R Paula 01/2017 6089 (2^350399+3618)/2 105481 Stefano Morozzi 09/2020 6090 (2^350379+1010)/2 105475 Stefano Morozzi 09/2020 6091 25233^15118+15118^25233 105462 Hans Havermann 09/2020 6092 26261^10366+10366^26261 105454 Hans Havermann 09/2020 6093 2^350307-110329 105453 Enzo Doria 05/2014 6094 2^350253-20365 105437 Enzo Doria 06/2013 6095 (3*29^72089-1075)/4 105423 Curtis Bright 05/2015 6096 (2^350187+2658)/2 105417 Stefano Morozzi 09/2020 6097 4*10^105415-69 105416 Robert Price 01/2022 6098 (22*10^105407+179)/3 105408 Robert Price 02/2022 6099 2^350139-109009 105403 Enzo Doria 04/2014 6100 (2^350129+3026)/2 105400 Stefano Morozzi 09/2020 6101 (2^350097+2070)/2 105390 Stefano Morozzi 09/2020 6102 3*5^150763+4 105380 Lelio R Paula 11/2014 6103 12^97643+91 105375 Lelio R Paula 02/2017 6104 6*5^150744-7 105367 Lelio R Paula 11/2014 6105 (2^350018+2074)/2 105366 Stefano Morozzi 09/2020 6106 4*10^105364-39 105365 Robert Price 09/2020 6108 2^349996-112169 105360 Enzo Doria 06/2014 6107 (2^349997+3702)/2 105360 Stefano Morozzi 09/2020 6109 (418*10^105343+23)/9 105345 Robert Price 02/2020 6110 25490^13563+13563^25490 105334 Hans Havermann 10/2020 6111 11^101142-1080 105329 Enzo Doria 12/2012 6112 (68*10^105320-41)/9 105321 Robert Price 10/2013 6113 24800^17649+17649^24800 105319 Hans Havermann 09/2020 6114 3^220712-9934 105307 Enzo Doria 05/2014 6115 7*10^105296+9 105297 Robert Price 09/2015 6116 89*10^105284-7 105286 Robert Price 04/2020 6117 2^349739+1873373 105282 Enzo Doria 06/2016 6118 7^124574+24 105278 Lelio R Paula 11/2016 6119 2^349708-20957 105273 Enzo Doria 06/2013 6120 34115^1218+1218^34115 105267 Hans Havermann 09/2020 6121 2^349649-20469 105255 Enzo Doria 06/2013 6122 2^349607-20109 105243 Enzo Doria 06/2013 6123 (85*10^105242+473)/9 105243 Robert Price 01/2020 6124 2^349594-19085 105239 Enzo Doria 05/2013 6125 2^349530+1874479 105220 Enzo Doria 06/2016 6126 (3^220528+8)/8081 105215 Lelio R Paula 12/2013 6127 (106*10^105199+17)/3 105201 Robert Price 04/2021 6128 (2^349452+3570)/2 105196 Stefano Morozzi 09/2020 6129 3^220464-112852 105189 Enzo Doria 07/2014 6130 2^349419-17349 105186 Enzo Doria 05/2013 6131 2^349400-2579 105180 Yves Minet 07/2014 6132 8*5^150471+3 105176 Lelio R Paula 11/2014 6133 (2^349359+2298)/2 105168 Stefano Morozzi 02/2021 6134 655^37342+37342^655 105165 Norbert Schneider 08/2018 6135 13^94403+94 105160 Lelio R Paula 12/2016 6136 2^349301-112309 105151 Enzo Doria 06/2014 6137 30291^2960+2960^30291 105149 Hans Havermann 09/2020 6138 27350^6981+6981^27350 105132 Hans Havermann 09/2020 6140 9*2^349220+5 105127 Lelio R Paula 09/2014 6139 (2^349225+3122)/2 105127 Stefano Morozzi 09/2020 6141 7*3^220317+8 105119 Lelio R Paula 09/2014 6142 7^124386+88 105119 Lelio R Paula 11/2016 6143 (2^349197+570)/2 105119 Stefano Morozzi 09/2020 6144 2^349171-19657 105111 Enzo Doria 06/2013 6145 (2^349115+590)/2 105094 Stefano Morozzi 09/2020 6146 (2^(6*58185+1)-5)/3 105093 Kevin Acres 11/2013 6147 (2^349111-5)/3 105093 Lelio R Paula 12/2013 6148 675^37142+37142^675 105087 Norbert Schneider 08/2018 6149 2^348981-2797573 105054 Enzo Doria 04/2016 6150 2^348869-6555 105021 Lelio R Paula 01/2017 6151 5^150217+78 104998 Lelio R Paula 11/2016 6152 (88*10^104989-1)/3 104991 Robert Price 04/2020 6153 (28*10^104972+149)/3 104973 Robert Price 12/2019 6154 24927^16262+16262^24927 104972 Hans Havermann 10/2020 6155 2^348703-113005 104971 Enzo Doria 06/2014 6156 (191*10^104956-17)/3 104958 Robert Price 11/2021 6158 2^348612-809 104943 Yves Minet 05/2013 6157 (73*10^104942-1)/9 104943 Robert Price 01/2015 6159 2^348583-350407 104934 Enzo Doria 06/2015 6160 2^348531-949 104919 Yves Minet 05/2012 6161 20^80636-59 104910 Lelio R Paula 12/2016 6162 8*10^104893-13 104894 Robert Price 08/2019 6164 2^348437+35 104890 Lelio R Paula 09/2011 6163 25208^14487+14487^25208 104890 Hans Havermann 09/2020 6165 2^348348+135 104864 Lelio R Paula 09/2011 6166 (29*10^104858+349)/9 104859 Robert Price 06/2021 6167 6*10^104852-31 104853 Robert Price 07/2020 6169 (2^348284+9)/25 104843 Lelio R Paula 12/2013 6168 75^55914-74 104843 Norbert Schneider 01/2015 6170 2^348268+255255 104840 Lelio R Paula 01/2017 6171 35540^891+891^35540 104839 Hans Havermann 09/2020 6172 5^149985-52 104836 Lelio R Paula 11/2016 6173 2^348224-20249 104826 Enzo Doria 06/2013 6174 (2^348217+2522)/2 104824 Stefano Morozzi 09/2020 6175 2^348212-20105 104823 Enzo Doria 06/2013 6176 24647^17898+17898^24647 104819 Hans Havermann 10/2020 6177 20^80562+19 104814 Lelio R Paula 12/2016 6178 2*10^104811-87 104812 Robert Price 04/2018 6179 2^348149-20053 104804 Enzo Doria 06/2013 6180 2^348095-171 104788 Lelio R Paula 09/2011 6181 25383^13412+13412^25383 104769 Hans Havermann 09/2020 6182 2^348003-20377 104760 Enzo Doria 06/2013 6183 2^347994-741 104757 Lelio R Paula 12/2016 6184 (2^347993+2234)/2 104757 Stefano Morozzi 01/2021 6185 (2^347990+790)/2 104756 Stefano Morozzi 09/2020 6186 25137^14702+14702^25137 104756 Hans Havermann 09/2020 6187 (13*2^347972-1)/282309 104746 Lelio R Paula 03/2014 6188 12883^25484-25484^12883 104740 Norbert Schneider 08/2022 6189 2^347910-109937 104732 Enzo Doria 04/2014 6190 (88*10^104709-637)/9 104710 Robert Price 11/2020 6191 (13*10^104702+71)/3 104703 Robert Price 06/2021 6192 5^149794+28 104702 Lelio R Paula 11/2016 6193 105^51800-2 104698 Lelio R Paula 10/2017 6194 (16^86939+3^86939)/19 104684 Robert Price 06/2013 6195 (15^89009-1)/14 104682 Paul Bourdelais 03/2010 6196 2^347731-18609 104678 Enzo Doria 05/2013 6197 4*6^134519+7 104677 Lelio R Paula 11/2014 6198 (34*10^104672-259)/9 104673 Robert Price 12/2021 6199 25321^13588+13588^25321 104656 Hans Havermann 09/2020 6200 2^347625+5367 104646 Riley Fisher 04/2023 6201 2^347612-18545 104642 Enzo Doria 05/2013 6204 6^134465+95 104635 Lelio R Paula 11/2016 6202 (2^347588+3718)/2 104635 Stefano Morozzi 09/2020 6203 (166*10^104633-7)/3 104635 Robert Price 11/2020 6205 2^347517-17301 104614 Enzo Doria 05/2013 6206 (2^347493+3186)/2 104606 Stefano Morozzi 09/2020 6207 (2^347490+2574)/2 104605 Stefano Morozzi 09/2020 6208 3^219222-310 104596 Lelio R Paula 11/2016 6209 25993^10554+10554^25993 104581 Hans Havermann 09/2020 6210 (15*2^347399-1)/13 104578 Lelio R Paula 03/2014 6211 2^347372-17853 104570 Enzo Doria 05/2013 6212 2^347314+99 104552 Lelio R Paula 09/2011 6213 2^347300-22233 104548 Enzo Doria 06/2013 6214 2^347287-19845 104544 Enzo Doria 06/2013 6215 2^347258-231191 104536 Harrison Mesh 06/2022 6216 (31*2^347254-1)/891 104533 Lelio R Paula 03/2014 6217 5*F(250091)*(F(250091)-1)+1 104532 Serge Batalov 04/2015 6218 7*2^347239-3 104531 Lelio R Paula 09/2014 6219 (3^219098-8)/514147439969 104525 Lelio R Paula 12/2013 6220 5*3^219047+8 104513 Lelio R Paula 09/2014 6221 2^347148-109073 104502 Enzo Doria 04/2014 6222 2^347129-20145 104497 Enzo Doria 06/2013 6223 4*10^104461-57 104462 Robert Price 10/2018 6224 (2^346989+590)/2 104454 Stefano Morozzi 09/2020 6225 2^346923-19585 104435 Enzo Doria 05/2013 6226 (11*2^346864-1)/175 104416 Lelio R Paula 03/2014 6227 2^346854+346854^2+1 104414 Robert Price 06/2014 6228 2^346834+11715 104408 Lelio R Paula 04/2015 6229 24276^19961+19961^24276 104392 Hans Havermann 09/2020 6230 79^55009+78 104387 Norbert Schneider 02/2015 6231 3^218744+58 104368 Lelio R Paula 11/2016 6232 9*10^104361+89 104362 Robert Price 11/2019 6233 25048^14665+14665^25048 104358 Hans Havermann 09/2020 6234 2^346649+65 104352 Lelio R Paula 09/2011 6235 (19*33^68718-600883)/32 104350 Eric Chen 05/2023 6236 2^346638-17265 104349 Enzo Doria 05/2013 6237 (2^346606+2082)/2 104339 Stefano Morozzi 09/2020 6238 (2^346607+2070)/2 104339 Stefano Morozzi 09/2020 6239 (2^346582+3202)/2 104332 Stefano Morozzi 09/2020 6240 26092^9967+9967^26092 104331 Hans Havermann 09/2020 6241 5*10^104326+77 104327 Robert Price 12/2018 6242 (2^346564+2026)/2 104326 Stefano Morozzi 09/2020 6245 2^346527-111817 104316 Enzo Doria 05/2014 6244 6^134055+101 104316 Lelio R Paula 11/2016 6243 fibonacci(499147)-4 104316 Jon Grantham 08/2023 6246 92105!4+8 104312 Robert Price 09/2019 6247 (7^123407-5^123407)/2 104291 Jon Grantham 08/2023 6248 6^134013+163 104283 Lelio R Paula 11/2016 6249 10^(2*52140+1)-10^52140-1 104281 Robert Price 07/2023 6250 (22*10^104272-61)/3 104273 Robert Price 03/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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